CE 394K.2 Hydrology
Infiltration
Reading AH Sec 5.1 to 5.5
Some slides were prepared by Venkatesh Merwade
Slides 2-6 come from
http://biosystems.okstate.edu/Home/mkizer/C%20Soil%20Water%20Relationships.ppt
Soil Water Measurement
• Neutron scattering (attenuation)
– Measures volumetric water content (v)
– Attenuation of high-energy neutrons by hydrogen nucleus
– Advantages:
• samples a relatively large soil sphere
• repeatedly sample same site and several depths
• accurate
– Disadvantages:
• high cost instrument
• radioactive licensing and safety
• not reliable for shallow measurements near the soil surface
• Dielectric constant
–
–
–
–
A soil’s dielectric constant is dependent on soil moisture
Time domain reflectometry (TDR)
Frequency domain reflectometry (FDR)
Primarily used for research purposes at this time
Soil Water Measurement
Neutron Attenuation
Soil Water Measurement
• Tensiometers
– Measure soil water potential (tension)
– Practical operating range is about 0 to 0.75
bar of tension (this can be a limitation on
medium- and fine-textured soils)
• Electrical resistance blocks
– Measure soil water potential (tension)
– Tend to work better at higher tensions (lower
water contents)
• Thermal dissipation blocks
– Measure soil water potential (tension)
– Require individual calibration
Tensiometer for Measuring Soil Water Potential
Water Reservoir
Variable Tube Length (12 in- 48 in)
Based on Root Zone Depth
Porous Ceramic Tip
Vacuum Gauge (0-100 centibar)
Electrical Resistance Blocks & Meters
Infiltration
• General
– Process of water
penetrating from
ground into soil
– Factors affecting
• Condition of soil
surface, vegetative
cover, soil properties,
hydraulic conductivity,
antecedent soil
moisture

Saturation Zone

Transition Zone
Transmission
Zone
Wetting Zone
– Four zones
• Saturated,
transmission, wetting,
and wetting front
Wetting Front
depth
Richard’s Equation
• Recall
– Darcy’s Law
– Total head
• So Darcy becomes
D K
h
z
h  z
q z  K
   z 
z
  

  K
K
  z

 

  D
K
 z

q z  K


Soil water diffusivity
• Continuity becomes 
t

q z  K
q   

 D
K
z z  z


K
z
Philips Equation
• Recall Richard’s
Equation
   

 D
K
t z  z

– Assume K and D are
functions of , not z
• Solution
– Two terms represent
effects of
• Suction head
• Gravity head
• S – Sorptivity
– Function of soil suction
potential
– Found from experiment
F (t )  St1/ 2  Kt
1 1/ 2
f (t )  St
K
2
Infiltration into a horizontal soil
column
Θ = Θo for x = 0, t > 0
Boundary conditions
Θ = Θn for t = 0, x > 0
x
0
Equation:

 

D
t x z
Measurement of Diffusivity by
Evaporation from Soil Cores
Air stream
q
x
q = soil water flux = evaporation rate

qD
x
Measurement of Diffusivity by
Evaporation from Soil Cores
http://www.regional.org.au/au/asa/2006/poster/water/4521_deeryd.htm
Numerical Solution of Richard’s
Equation
(Ernest To)
http://www.ce.utexas.edu/prof/maidment/GradHydro2007/Ex4/Ex4Soln.doc
Implicit Numerical Solution of
Richard’s Equation
t (j)
j
j -1
x (i)
i-1 i i+1
Implicit Numerical Solution of
Richard’s Equation
Matrix solution of the equations
Θ
f
F
Definitions
V  gross volume of element
Vv  volume of pores
Element of soil, V
(Saturated)
Pore with
water
solid
Vs  volume of solids
Vw  volume of water
Vv
n   porosity
V
Vw
S
 saturation; 0  S  1
Vv
V
  w  nS  moisture content; 0    n
V
Pore with
air
Element of soil, V
(Unsaturated)
Infiltration
• Infiltration rate
f (t )
– Rate at which water enters the soil at the surface
(in/hr or cm/hr)
• Cumulative infiltration
– Accumulated depth of water infiltrating during given
time period
t
F (t )   f ( )d
0
f (t ) 
dF (t )
dt
Infiltrometers
Single Ring
Double Ring
http://en.wikipedia.org/wiki/Infiltrometer
Infiltration Methods
• Horton and Phillips
– Infiltration models developed as approximate
solutions of an exact theory (Richard’s
Equation)
• Green – Ampt
– Infiltration model developed from an
approximate theory to an exact solution
Hortonian Infiltration
• Recall Richard’s
Equation
– Assume K and D are
constants, not a function
of  or z
• Solve for moisture
diffusion at surface
   

 D
K
t z  z


 2 K
D 2 
t
z
z

 2
D 2
t
z
0
f (t )  f c  ( f 0  f c )e kt
f0 initial infiltration rate, fc is constant rate and k is decay constant
Hortonian Infiltration
3.5
f0
3
Infiltration rate, f
2.5
k1
2
k1 < k2 < k3
1.5
k2
1
k3
fc
0.5
0
0
0.5
1
Time
1.5
2
Philips Equation
• Recall Richard’s
Equation
   

 D
K
t z  z

– Assume K and D are
functions of , not z
• Solution
– Two terms represent
effects of
• Suction head
• Gravity head
• S – Sorptivity
– Function of soil suction
potential
– Found from experiment
F (t )  St1/ 2  Kt
1 1/ 2
f (t )  St
K
2
Green – Ampt Infiltration
L  Depth to Wetting Front
 i  Initial Soil Moisture
Ponded Water
h0

Ground Surface
F (t )  L(  i )  L
Wetted Zone
dF
dL
f 
 
dt
dt
Wetting Front
h
q z  K
f
z
i

h  z
f K

K
z
n
z
Dry Soil
L
Green – Ampt
Infiltration (Cont.)
f K
Ground Surface
Wetted Zone

K
z
Wetting Front
• Apply finite difference to the
derivative, between
– Ground surface z  0,  0
– Wetting front z  L,   f
 f 0


f K
K K
K K
K
z
z
L0
F (t )  L
F
L

 
f  K 
 F

f

 1

i


z
Dry Soil

f K
K
z
L
Green – Ampt
Infiltration (Cont.)
 
f  K 
 F
f

 1

f  
Ground Surface
Wetted Zone
dL
dt
i


 f

dL
 K 
 1
dt
 L

 f dL
K
dt dL 

 f L
Integrate
K
t L  f ln( f  L)  C

L
Wetting Front
F (t )  L


z
Dry Soil
Evaluate the constant of integration
L  0 @t  0
C   f ln( f )
Kt L   f ln(
f
 f L
)
Green – Ampt Infiltration
(Cont.)
Kt L   f ln(
f
 f L
Ground Surface

Wetted Zone
Wetting Front
)
i


F  Kt   f ln(1 
 
f  K 
 F
f

 1

F
 f
)
z
Dry Soil
Nonlinear equation, requiring iterative solution.
See: http://www.ce.utexas.edu/prof/mckinney/ce311k/Lab/Lab8/Lab8.html
L
Soil Parameters
• Green-Ampt model requires
– Hydraulic conductivity, Porosity, Wetting Front
Suction Head
– Brooks and Corey
se 
 r
e
e  n  r
Effective saturation
Soil Class
Porosity
Effective
Porosity
n
e
Effective porosity
  (1  se ) e
Sand
Loam
Clay
0.437
0.463
0.475
0.417
0.434
0.385
Wetting
Front
Suction
Head

(cm)
4.95
9.89
31.63
Hydraulic
Conductivity
K
(cm/h)
11.78
0.34
0.03
Ponding time
• Elapsed time between the time rainfall
begins and the time water begins to pond
on the soil surface (tp)
• Up to the time of ponding,
all rainfall has infiltrated (i
= rainfall rate)
Potential
Infiltration
Rainfall
i
F  i *t p
 
f  K 
 F
f

 1

  f

i  K
 1
 i *t p



 f
tp K
i (i  K )
Actual Infiltration
Accumulated
Rainfall
Cumulative
Infiltration, F
f i
Infiltration rate, f
Ponding Time
Time
Infiltration
Fp  i * t p
tp
Time
Example
• Silty-Loam soil, 30%
effective saturation,
rainfall 5 cm/hr
intensity
 e  0.486
  16.7 cm
K  0.65 cm / hr
se  0.30
  (1  se ) e  (1  0.3)(0.486)  0.340
  16.7 * 0.340
tp K
 f
i (i  K )
 0.65
5.68
 0.17 hr
5.0(5.0  0.65)(i  K )